A New Kind of Science: The NKS Forum > Applied NKS > Fluid flows
Author
Stuart Munro

Registered: Nov 2003
Posts: 1

Fluid flows

I have some questions regarding the images on page 378 of NKS:

1. What happens at the edges of the diagram? Are particles which pass across the top and bottom of the plot lost forever?

2. When it says that 'particles are inserted at 1/3 of the maximum speed possible', what exactly does this mean and how is it achieved?

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11-19-2003 06:37 AM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Sorry it took so long to get answers to your straightforward questions. The original work on this was done quite a while ago and I didn't personally know the answers as to how it was actually set up, that is the only reason for the delay.

Particles leaving the top or bottom return on the bottom or top - it is effectively a wrapped around cylinder aka periodic boundary on those sides. Particles that leave the right or left (mostly right, as it is set up) are gone.

The speed at the lowest level is always 1 or 0 in any of the directions allowed by the lattice - there is no numerical speed kept at each point on the grid. Differing speeds arise at a higher level (in averages e.g.) from not all particles moving in the same direction.

The insertion of new particles from the left is said to occur at 1/3rd of the maximum possible speed. Maximum possible would mean a new particle at every step at every vertical location on the left hand edge. Less than the maximum possible speed means fewer than this maximum possible number of particles enter.

At each vertical position you either get a particle or you don't, and you get one at a third of the vertical positions on each step. On the next step, you get them at a different set of vertical positions. Same on a third step, then you are back to the original set of input positions. So it is cyclic-deterministic 1/3, not random 1/3.

If particles are moving leftward next to the left hand edge, the usual collision rules apply and may "scatter" the input particles. Note also that on a hexagonal (not square) grid, there are 2 right-moving directions, right-up and right-down, for the new particles to come in.

I hope this is what you were after. I believe Oyvind Tajford has worked on this stuff the most recently, among the Wolfram Science Group people. If you have additional detailed questions, I'll answer if I know and can ping him if I don't.

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12-13-2003 05:44 AM
Alejandro Vizcarra
Zacatecas University
Mexico

Registered: Mar 2005
Posts: 1

turbulence

Is it possible to get the programs necesary to reproduce the images in AKS page 380?

I have the basic programs for fluid flow and I am trying to include obstacles and flow. However I am not yet very good programming in Mathematica.

I will be most thankfull for any help with this matter!

__________________
Alejandro Vizcarra
gebankos@prodigy.net.mx

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03-01-2005 12:57 PM

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